Question 1193410: 1. Julita owes Jose the following amounts:
a. 55,000 at the end of 4 years,
b. 48,000 at the end of 5 years, and
c. 75,000 due in 3 years from today at 9% converted quarterly.
What single payment at the end of 2 years will settle Julita’s
obligations if money is worth 15% converted monthly?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Calculate the Present Value of Each Obligation at the End of 2 Years**
* **Obligation a: 55,000 at the end of 4 years**
* Time to maturity from the end of 2 years: 4 - 2 = 2 years
* Present Value (PV_a) = 55,000 / (1 + 0.15/12)^(2*12)
* **Obligation b: 48,000 at the end of 5 years**
* Time to maturity from the end of 2 years: 5 - 2 = 3 years
* Present Value (PV_b) = 48,000 / (1 + 0.15/12)^(3*12)
* **Obligation c: 75,000 due in 3 years from today at 9% converted quarterly**
* Time to maturity from today: 3 years
* Time to maturity from the end of 2 years: 3 - 2 = 1 year
* Effective annual rate for quarterly compounding: (1 + 0.09/4)^4 - 1 = 0.093083
* Present Value (PV_c) = 75,000 / (1 + 0.093083)^1 * (1 + 0.15/12)^(-12)
**2. Calculate the Total Present Value of All Obligations at the End of 2 Years**
* Total Present Value = PV_a + PV_b + PV_c
**3. Determine the Single Payment at the End of 2 Years**
* The single payment at the end of 2 years to settle all obligations is equal to the total present value of all obligations at that time.
**Using Python:**
```python
import numpy as np
# Calculate the present value of each obligation at the end of 2 years
# Obligation a: 55,000 at the end of 4 years
# Time to maturity from the end of 2 years: 4 - 2 = 2 years
pv_a = 55000 / (1 + 0.15/12)**(2*12)
# Obligation b: 48,000 at the end of 5 years
# Time to maturity from the end of 2 years: 5 - 2 = 3 years
pv_b = 48000 / (1 + 0.15/12)**(3*12)
# Obligation c: 75,000 due in 3 years from today at 9% converted quarterly
# Time to maturity from today: 3 years
# Time to maturity from the end of 2 years: 3 - 2 = 1 year
# Effective annual rate for quarterly compounding: (1 + 0.09/4)**4 - 1 = 0.093083
pv_c = 75000 / (1 + 0.093083)**1 * (1 + 0.15/12)**(-12)
# Total present value of all obligations at the end of 2 years
total_pv = pv_a + pv_b + pv_c
print(f"Single payment at the end of 2 years to settle Julita's obligations: {total_pv:.2f}")
```
**Result:**
The single payment at the end of 2 years to settle Julita's obligations is approximately **130,623.40**.
Answer by ikleyn(52775)  (Show Source):
You can put this solution on YOUR website! .
I can not leave this problem and its solution without my notices.
The problem itself looks very strange to me.
(1) It systematically repeats "converted" instead of "compounded", which tells me
that the author is unfamiliar with standard terminology - so the author is a person who accidentally got lost.
(2) From the problem, it is unclear, to which money this statement relates "If money is worth 15% converted monthly".
Honestly, my impression is that the condition of the problem is mistakenly mixed
from two different problems (so the author accidently was got lost again).
(3) In the solution, calculation for pv_c looks strange to me.
It uses the formula
pv_c = 75000/(1+0.093083)^1*(1+0.15/12)^(-12)
It seems out of logic, since all we need to do in this part is to rewind back one year from 75,000
with the quarterly compounding effective rate r = 0.09/4,
so the formula should be
pv_c = 75000/(1+0.09/4)^4,
which will produce, definitely, another value.
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